The two parts of definition 1 cover most of how I've seen it used, with definition 2 perhaps explaining something about bard songs.

There's a couple of things that aren't addressed in the definition. One is that charisma (afaik) affects the prices shopkeepers give you when you're haggling. Another is that the charisma of a group leader seems to affect the morale of the group members.

Both of those are personality based, not appearance based, but at the same time can't be easily reflected simply by how someone roleplays their character. This sort of thing is why most dice and paper RPGs keep at least one personality based trait. You may act like an ass yet people like you anyway, or you may be the nicest and most hated person around. Both happen in the real world quite often.

Personally, my RP eventually reflects the charisma stat to a degree, but it also reflects the rest of the stats as well. But without a true appearance stat that aspect ends up however I feel fits the characterization of the character.